A Field Range Bound for General Single-Field Inflation

TL;DR

This paper generalizes the Lyth bound for single-field inflation models, demonstrating that non-trivial dynamics cannot evade it, and establishes a universal bound under the Null Energy Condition.

Contribution

It introduces a generalized Lyth bound applicable to all single-field inflation models with two-derivative kinetic terms, strengthening previous bounds and exploring implications of primordial tensor detection.

Findings

The generalized bound applies broadly to single-field models.

Non-trivial dynamics cannot bypass the Lyth bound.

A universal bound holds under the Null Energy Condition.

Abstract

We explore the consequences of a detection of primordial tensor fluctuations for general single-field models of inflation. Using the effective theory of inflation, we propose a generalization of the Lyth bound. Our bound applies to all single-field models with two-derivative kinetic terms for the scalar fluctuations and is always stronger than the corresponding bound for slow-roll models. This shows that non-trivial dynamics can't evade the Lyth bound. We also present a weaker, but completely universal bound that holds whenever the Null Energy Condition (NEC) is satisfied at horizon crossing.